Question: Solve for $x$ and $y$ using elimination. ${-5x-2y = -37}$ ${2x+y = 15}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the bottom equation by $2$ ${-5x-2y = -37}$ $4x+2y = 30$ Add the top and bottom equations together. $-x = -7$ $\dfrac{-x}{{-1}} = \dfrac{-7}{{-1}}$ ${x = 7}$ Now that you know ${x = 7}$ , plug it back into $\thinspace {-5x-2y = -37}\thinspace$ to find $y$ ${-5}{(7)}{ - 2y = -37}$ $-35-2y = -37$ $-35{+35} - 2y = -37{+35}$ $-2y = -2$ $\dfrac{-2y}{{-2}} = \dfrac{-2}{{-2}}$ ${y = 1}$ You can also plug ${x = 7}$ into $\thinspace {2x+y = 15}\thinspace$ and get the same answer for $y$ : ${2}{(7)}{ + y = 15}$ ${y = 1}$